A new thin layer model for viscous flow between two nearby non-static surfaces

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A new thin layer model for viscous flow between two nearby non-static surfacesDate
2023Citation
Rodríguez, J. M., Taboada‐Vázquez, R. (2023). A new thin layer model for viscous flow between two nearby non‐static surfaces. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 103(12), e202200571. https://doi.org/10.1002/zamm.202200571
Abstract
[Abstract:] We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes equations. The leading term of the formal asymptotic expansions of the solutions to the new model and Navier-Stokes equations are solution of the same limit problem, and the type of the limit problem depends on the boundary conditions. If slip velocity boundary conditions are imposed on the upper and lower bound surfaces, the limit is a solution of a lubrication model, but if the tractions and friction forces are known on both bound surfaces, the limit is a solution of a thin fluid layer model. The model proposed has been obtained to be a valuable tool for computing viscous fluid flow between two nearby moving surfaces, without the need to decide a priori whether the flow is typical of a lubrication or a thin fluid layer problem, and without the enormous computational effort that would be required to solve the Navier-Stokes equations in such a thin domain.
Keywords
Fluid mechanics
Lubrication
Thin fluid layer
Asymptotic analysis
Lubrication
Thin fluid layer
Asymptotic analysis
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Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG
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Atribución-NoComercial-SinDerivadas 3.0 España